Une introduction accessible à la « Connaissance par Morceaux »

La Connaissance par Morceaux(CpM) est une perspective épistémologique qui a réussi à produire, dans le champ de la didactique des sciences, des explications significatives de phénomènes d’apprentissage, en particulier en ce qui concerne les conceptions préalables des élèves et les rôles de celles-ci dans l’émergence de la compétence. La CpM est nettement moins utilisée en mathématiques. Cependant, je fais l’hypothèse que les raisons de ce moindre usage relèvent principalement de différences historiques plutôt que d’écarts entre les processus d’apprentissage en mathématiques et en sciences expérimentales. L’objectif de cet article est de présenter la CpM d’une manière relativement accessible pour des chercheurs en didactique des mathématiques. Je présente les principes généraux et les caractéristiques essentielles de la CpM. Je m’appuie sur une variété d’exemples, y compris d’exemples en mathématiques, pour illustrer le fonctionnement de la CpM, son utilisation pratique et ce que l’on peut en attendre. J’espère ainsi encourager et accompagner une utilisation plus importante de la CpM dans la recherche en didactique des mathématiques.Knowledge in Pieces (KiP) is an epistemological perspective that has had significant success in explaining learning phenomena in science education, notably the phenomenon of students’ prior conceptions and their roles in emerging competence. KiP is much less used in mathematics. However, I conjecture that the reasons for relative disuse mostly concern historical differences in traditions rather than in-principle distinctions in the ways mathematics and science are learned.This article aims to explain KiP in a relatively non-technical way to mathematics educators. I explain the general principles and distinguishing characteristics of KiP. I use a range of examples, including from mathematics, to show how KiP works in practice and what one might expect to gain from using it. My hope is to encourage and help guide a greater use of KiP in mathematics education

Transitions in Mathematics Education

Mathematics Education; Learning; Teachin

On "Learnable" Representations of Knowledge: A Meaning for the Computational Metaphor

The computational metaphor which proposes the comparison of processes of mind to realizable or imaginable computer activities suggests a number of educational concerns. This paper discusses some of those concerns including procedural modes of knowledge representation and control knowledge ??owing what to do. I develop a collection of heuristics for education researchers and curriculum developers which are intended to address the issues raised. Finally, an extensive section of examples is given to concretize those heuristics

Insegnare il Moto con Boxer

Descrizione di un corso sulla matematica del moto basato sulla premessa che tutte le persone coinvolte - studenti, insegnanti e progettisti - dovrebbero conoscere un computational medium generale e progammabile, Boxer

The construction of causal schemes: learning mechanisms at the knowledge level.

This work uses microgenetic study of classroom learning to illuminate (1) the role of pre-instructional student knowledge in the construction of normative scientific knowledge, and (2) the learning mechanisms that drive change. Three enactments of an instructional sequence designed to lead to a scientific understanding of thermal equilibration are used as data sources. Only data from a scaffolded student inquiry preceding introduction of a normative model were used. Hence, the study involves nearly autonomous student learning. In two classes, students developed stable and socially shared explanations ("causal schemes") for understanding thermal equilibration. One case resulted in a near-normative understanding, while the other resulted in a non-normative "alternative conception." The near-normative case seems to be a particularly clear example wherein the constructed causal scheme is a composition of previously documented naïve conceptions. Detailed prior description of these naive elements allows a much better than usual view of the corresponding details of change during construction of the new scheme. A list of candidate mechanisms that can account for observed change is presented. The non-normative construction seems also to be a composition, albeit of a different structural form, using a different (although similar) set of naïve elements. This article provides one of very few high-resolution process analyses showing the productive use of naïve knowledge in learning